A restored sense of purpose for Tate Britain ... a visitor at the gallery's new Millais show. Photograph: Christian Sinibaldi

Good exhibitions come and go, but a run of them starts to tell you something about the museum responsible. Tate Britain's new retrospective of the Victorian painter John Everett Millais is a major re-examination of 19th-century art.

Not everyone will be convinced by it - but no one can complain this museum is failing to champion the achievements of British artists in history. I found it excellent, in fact inspiring. It totally avoids the kinds of side issues - from ideology to scholarly fussing - that have sometimes loomed frustratingly large at Tate Britain. The truly amazing thing, however, is that Millais is the third brilliant historical exhibition here in the last 12 months - just a year ago they were opening Holbein and then came Hogarth.

These have all been exhibitions with backbones, and taken together give the museum a spine, that is, a sense of purpose. The curators obviously love their subjects (in Millais' case perhaps eccentrically so - and that's praise). All three exhibitions take a fascinating artist and give that artist's work a chance to shine. In all three cases, there is a sudden, exciting start rather than a long preamble: practically the first thing you saw in the Holbein exhibition was the German master's stupendous drawing of Thomas More. Similarly, with Hogarth you were right there in 18th-century London from start to finish. These are unpretentious, unpompous exhibitions that allow you to look at great art close up, in a calm, intelligent sequence of rooms.

It's obvious, after such a run of excellence, that Tate Britain - so often criticised since it was severed from Tate Modern - is hitting its stride. I have been irritated beyond belief by its refusal to simply, intelligently show off the largest collection of British art in the world. But with this programme of exhibitions Tate Britain is brilliantly showing us how much wonderful - and strange - stuff lies in our artistic attic. It's doing its job, in other words - superbly.